VolBond
Pieter Pijls
6 April 2018
Load packages
Import Data
First, I import the swap rate curves from 2002 to 2018.
# Import Data (swap rates)
setwd("C:/PIETER/INTERNSHIP P&V/Volbond")
rates <- read.xlsx("./EURIBOR vanilla interest rate swap contract.xlsx",colNames=TRUE,sheet=1)
# create date object
rates$DATE <- seq(as.Date("2001/1/1"), by = "month", length.out = 206)
rates20 <- as.data.frame(cbind(seq(as.Date("2001/1/1"), by = "month", length.out = 206), rates$`20`))
rates20$V1 <- as.Date(rates20$V1)We plot the evolution of the swap rate of 20Y.
# plot evolution swap rate 20y
g <- ggplot(rates20, aes(x=rates20$V1,y=rates20$V2)) + geom_line() + ggtitle("Evolution swap rate 20Y") +
xlab("Date") + ylab("Rate")
ggplotly(g)## We recommend that you use the dev version of ggplot2 with `ggplotly()`
## Install it with: `devtools::install_github('hadley/ggplot2')`Volbond data
We import data for the Volbond. The first column is the date, the second is the CMS rate 20Y in advance. The third column corresponds with the CMS 20Y rate in Arrears. The final column is the coupon which is equal to 3.5*absolute_value(CMS20Y in Advance - CMS20Y in Arrears).
# Import data for the Volbond
volbond20 <- rates <- read.xlsx("./Volbond20Y.xlsx",colNames=TRUE,sheet=1)
volbond20$DATE <- seq(as.Date("2001/1/1"), by = "month", length.out = 206)
volbond20 <- volbond20[-1,]
tail(volbond20)## DATE Advanced Arrears Coupon
## 201 2017-09-01 0.01552997 0.01419720 0.028423968
## 202 2017-10-01 0.01484673 0.01552997 0.017451072
## 203 2017-11-01 0.01469873 0.01484673 0.008950262
## 204 2017-12-01 0.01458644 0.01469873 0.008632111
## 205 2018-01-01 0.01555128 0.01458644 0.005047491
## 206 2018-02-01 0.01605061 0.01555128 0.011644508We plot the evolution of the CMS rate 20y and the Volbond coupon.
g <- ggplot(volbond20, aes(x=volbond20$DATE)) + geom_line(aes(y=volbond20$Advanced, colour = "CMS20Y")) + geom_line(aes(y=volbond20$Coupon, colour = "Coupon (%)")) + ggtitle("Evolution swap rate 20Y") +
xlab("Date") + ylab("Rate") + theme_bw()
ggplotly(g)## We recommend that you use the dev version of ggplot2 with `ggplotly()`
## Install it with: `devtools::install_github('hadley/ggplot2')`Next we create a histogram of the coupons
hist(volbond20$Coupon, breaks=20, xlab = "Coupon (%)")
We also have some summary stats.
# summary statistics coupons
summary(volbond20$Coupon)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.000369 0.007881 0.015886 0.018151 0.025848 0.065053 11The standard deviation is equal to
# standard deviation
sd(volbond20$Coupon[12:nrow(volbond20)])## [1] 0.01339778Example without shout option
In this example we calculate the payoff of the Volbond. We assume that we started investing in the Volbond in January 2001. The first coupon is paid out in January 2002. The last coupon is received in January 2016. We let the shout option outside the analysis.
#1# Example without shout option
n = 10000000 # Investment of 10mio
t = 15 # duration bond
coupon <- matrix(ncol = 3,nrow=t)
for (i in 1:t) # nyears(volbond20$DATE)
{
coupon[i,1] <- as.Date(volbond20$DATE[12*i])
coupon[i,2] <- volbond20$Coupon[12*i]
coupon[i,3] <- coupon[i,2]*n
}
as.Date(coupon[,1])## [1] "2002-01-01" "2003-01-01" "2004-01-01" "2005-01-01" "2006-01-01"
## [6] "2007-01-01" "2008-01-01" "2009-01-01" "2010-01-01" "2011-01-01"
## [11] "2012-01-01" "2013-01-01" "2014-01-01" "2015-01-01" "2016-01-01"The total return of this investment is equal to 24%.
# total return
totalreturn <- (sum(coupon[,3])+n)/n
totalreturn## [1] 1.246504The yearly return is equal to 1.479%.
# yearly return
yearlyreturn <- totalreturn^(1/t)-1
yearlyreturn## [1] 0.01479796Example with shout option (e.g. lock in rate from 3%)
In this example we incorporate the feature of the shout option. We assume management will lock in the rate when the previous coupon rate was higher as 3%. Again we assume that we started investing in the Volbond in January 2001. The first coupon is paid out in January 2002. The last coupon is received in January 2016.
n = 10000000 # Investment of 10mio
t = 15 # duration bond
shout = 0.03 # treshhold when rate is locked in
couponshout <- matrix(ncol = 3,nrow=t)
for (i in 1:t) # nyears(volbond20$DATE)
{
couponshout[i,1] <- as.Date(volbond20$DATE[12*i], format="%y-%m-%d")
couponshout[i,2] <- volbond20$Coupon[12*i]
couponshout[i,3] <- couponshout[i,2]*n
}
# loop to lock in values higher as 3%
for (i in 2:t)
{
if (couponshout[i-1,2]>shout)
{
couponshout[i,2] = couponshout[i-1,2]
couponshout[i,3] = couponshout[i-1,3]
}
else
{
couponshout[i,2] = couponshout[i,2]
couponshout[i,3] = couponshout[i,3]
}
}
colnames(couponshout) <- c("Date","Coupon (%)", "Coupon in ???")
couponshout## Date Coupon (%) Coupon in ???
## [1,] 11688 0.015341320 153413.20
## [2,] 12053 0.019497818 194978.18
## [3,] 12418 0.009036181 90361.81
## [4,] 12784 0.032724167 327241.67
## [5,] 13149 0.032724167 327241.67
## [6,] 13514 0.032724167 327241.67
## [7,] 13879 0.032724167 327241.67
## [8,] 14245 0.032724167 327241.67
## [9,] 14610 0.032724167 327241.67
## [10,] 14975 0.032724167 327241.67
## [11,] 15340 0.032724167 327241.67
## [12,] 15706 0.032724167 327241.67
## [13,] 16071 0.032724167 327241.67
## [14,] 16436 0.032724167 327241.67
## [15,] 16801 0.032724167 327241.67The total return is higher as we lock in the rate in from January 2005.The coupon is equal to \(327.241\) euro when we would invest \(10\) mio euro. Therefore the total return is higher compared with the example where we do not use the shout option. When we use the shout option on the right moment we can increase significantly the return on our investment.
# total return
totalreturn <- (sum(couponshout[,3])+n)/n
totalreturn## [1] 1.436565The yearly return is equal to
# yearly return
yearlyreturn <- totalreturn^(1/t)-1
yearlyreturn## [1] 0.02444432Different starting dates for the VolBond (without shout option)
In this analysis we use thirteen different starting dates from JAN01,FB01,MAR01,… to FEB02. Therefore, the first column corresponds with the coupon in % when we start investing in January 2001. The second column corresponds with the coupon % when we started investing in February 2001. We calculate the total and yearly return for different staring dates. In this example we do not use the shout option.
n = 10000000 # Investment of 10mio
t = 15 # duration bond
coupon <- matrix(ncol = 13, nrow=t)
# loop over different starting dates
for (j in 1:13)
{
# loop over coupon pay outs
for (i in 1:t) # nyears(volbond20$DATE)
{
coupon[i,j] <- volbond20$Coupon[(12*i)+j]
}
}
colnames(coupon)<- as.Date(volbond20$DATE[13:25]) The total returns for the different starting dates from JAN01,FB01,MAR01,… to FEB02 are equal to. The lowest return is 22.9%, the maximum is 33.2%.
# total return
totalreturn <- colSums(coupon)
totalreturn## 11719 11747 11778 11808 11839 11869 11900
## 0.2384969 0.2369824 0.2707814 0.3373220 0.3320158 0.2717943 0.3307751
## 11931 11961 11992 12022 12053 12084
## 0.2802229 0.2297074 0.2353639 0.3109268 0.2369288 0.2393373# yearly return
yearlyreturn <- (1+totalreturn)^(1/t)
yearlyreturn## 11719 11747 11778 11808 11839 11869 11900 11931
## 1.014362 1.014279 1.016104 1.019567 1.019297 1.016158 1.019233 1.016605
## 11961 11992 12022 12053 12084
## 1.013881 1.014191 1.018213 1.014276 1.014408The average yearly return is 1.6%. The maximum return is 2% while the minimum return is 1.4%.
summary(yearlyreturn)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.014 1.014 1.016 1.016 1.018 1.020